What is the Centripetal Acceleration of a Stone in Circular Motion?

[saber1357]

Homework Statement

A boy whirls a stone in a horizontal circle of radius 1.5 m and at a height of 2.0 m above level ground. The string breaks, and the stone flies off horizontally and strikes the ground after traveling a horizontal distance of 10 m. What is the magnitude of the centripetal acceleration of the stone during the circular motion?

Homework Equations

T = (2*3.14*r) / v^2
Ac = v^2 / r

The Attempt at a Solution

I am not even sure how to begin this problem. I do have the vertical and horizontal positions, but I do not know how to derive the velocity simply from the information given.
What am I missing?

 

[Leong]

1. projectile motion in 2d: find the initial horizontal velocity.
2. put the value in your second formula.

 

[D H]

You are missing gravity. You know that: (1) The height of the rock when the string broke, (2) The rock flew off horizontally when the string broke, and (3) It hit the ground after flying 10 meters. What does this tell you about the rock's velocity at the time the string broke?

 

[saber1357]

Ohhh snaap!
Lots of <3 DH, i didn't realize it flew horizontally!

 

[D H]

Did you read your own problem statement? The string breaks, and the stone flies off horizontally ...

 

[saber1357]

One last quick question. When I have acquired the Time, and I try to solve for horizontal initial velocity, is the equation Sx = Ux*t or Sx = Ucos(theta)*t? (U meaning initial velocity)
I'm terribly sorry DH, I read it but did not interpret it.

 

[D H]

You are missing one key assumption: The rock initially undergoes uniform circular motion.

Some questions:

• What does "uniform circular motion" mean in terms of the speed (as opposed to velocity) of the rock?
• Ignoring gravity, what happens to the rock when the string breaks? (Apply Newton's first of motion.)
• Now put gravity back into play. If the rock were dropped from 2 meters above the ground, how long would it take for the rock to hit the ground?
• How long does it take the rock to hit the ground from 2 meters above the ground if you throw it horizontally?
• What horizontal velocity is needed to make the rock hit the ground 10 meters from the release point?
• Now put the circular motion back into play: what centripedal acceleration is needed to make the rock have the velocity given in the above answer?

 

[saber1357]

Oh I see, so since it was moving at a horizontal motion, the supposed theta is 0, meaning the horizontal position simply equals initial velocity * time! It's so simple, thank you DH.